Suppose line z intersects lines x & y at two different points,but is not a transversal.Explain how this is?

Question

possible.

Answer 1

The answer depends on how you define "transversal". In a narrow definition a transversal line crosses parallel lines. If they are not parallel then the line crossing them is not a transversal line.

Wikipedia defines it this way.

http://en.wikipedia.org/wiki/Transversal_line

In geometry, a transversal line is a line that passes through two or more other coplanar lines at different points, especially when the other coplanar lines are also parallel.
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If you use a broader definition of transversal this is not possible. The broad definition simply requires the transversal line to cross the other lines. They don't need to be parallel.

MathWorld defines it this way.

http://mathworld.wolfram.com/TransversalLine.html

A transversal line is a line which intersects each of a given set of other lines. It is also called a semisecant.

Answer 2

Of course, because both equations behave according to their respective slope as defined by their coordinates, Assign X=0 and solve for Y and vice versa, do this to each linear equation then plot the lines as defined by ( 0,Y) and ( X,0) coordinates. In fact we've learned from plane geometry that parallel lines never intersect to each other. Therefore all lines in a single plain intersect each other except parallel lines.

Answer 3

becouse z is in the center